Let a, b in R be such that a, a + | vedclass

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Question

We have, $2(a+2 b)=a+(2 a+b)$

$\Rightarrow {a}=3 {b}$      ...$(1)$

and $(a b+5)^{2}=(a+1)^{2}(b+1)^{2}$      ....

Vedclass · Accepted Answer

$4$

Vedclass · Answer

We have, $2(a+2 b)=a+(2 a+b)$

$\Rightarrow {a}=3 {b}$      ...$(1)$

and $(a b+5)^{2}=(a+1)^{2}(b+1)^{2}$      ....$(2)$

$	herefore$ Using $( 1)$ in $(2),$ we get

$\left(3 b^{2}+5ight)^{2}=(3 b+1)^{2}(b+1)^{2}$

$\Rightarrow 3 b^{2}+5=\pm(3 b+1)(b+1)$

$	herefore 3 b^{2}+5=3 b^{2}+4 b+1$

$\Rightarrow \mathrm{b}=1 \quad$ or $\quad 3 \mathrm{b}^{2}+5=-3 \mathrm{b}^{2}-4 \mathrm{b}-1$

$\Rightarrow \underbrace{3 b^{2}+2 b+3=0}_{	ext {Disc. }<0} \cdot$ so $b 
otin R$

So ${b}=1, {a}=3 .$ Hence $({a}+{b})=4$

Let $a$, $b \in R$ be such that $a$, $a + 2b$ , $2a + b$ are in $A.P$. and $(b + 1)^2$, $ab + 5$, $(a + 1)^2$ are in $G.P.$ then $(a + b)$ equals

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